[Question] alternative history: what if Bayes rule had never been discovered?

In try­ing to un­der­stand how Bayesian prob­a­bil­ity is used, I’m cu­ri­ous to know what wouldn’t have been pos­si­ble with­out it. how im­por­tant was it in the course of hu­man dis­cov­ery, and in turn, how it effected his­tory.

I don’t de­mand rigor­ous an­swers, feel free to spec­u­late and throw pos­si­bil­ities as you like.

Bonus ques­tion: if Bayes didn’t dis­cover it, when would it have to be dis­cov­ered? (full spec­u­la­tion mode)

There’s no way it wouldn’t have been dis­cov­ered. The math­e­mat­ics is sim­ple, and “in­verse prob­a­bil­ity” (as it was called then) is a ma­jor part of what is done with prob­a­bil­ity and statis­tics.

I’m tempted to spec­u­late about a “harder” ver­sion of this ques­tion: what if we lived in a uni­verse where Bayes’ the­o­rem not only hand’t been dis­cov­ered but wasn’t true? Like a uni­verse with differ­ent physics of causal­ity. But I digress.

I don’t have a di­rect an­swer for you, but it might be con­struc­tive to re­flect that Bayes’ the­o­rem is a par­tic­u­lar math­e­mat­i­cal un­der­stand­ing of a pat­tern peo­ple un­der­stand and use im­plic­itly and pops up all over the place be­cause Bayes’ is a view onto the mechanisms of cau­sa­tion. This sug­gests that even with­out Bayes’ the­o­rem for­mally stated by any­one in any way, we’d still see it pop up all over the place, only no one would have iden­ti­fied it as a com­mon pat­tern.

Yes, it’s a good point, that it’s a pat­tern that will pop up all over the place re­gard­less. so the ques­tion is, if no one for­mally stated it (i.e iden­ti­fied it as a com­mon pat­tern), how would it look? what sci­en­tific dis­cov­er­ies wouldn’t have been made? what wouldn’t have been in­vented? what would we have be­lieved to be true that’s ac­tu­ally false? what bad de­ci­sions would we make? what good de­ci­sion have we made be­cause of it that we would have been able to make with­out it?